CrimsonKidCK:
AFAIK it's unethical to use another author's characters without his/her express permission.
The legal position on this is straightforward, but tricky in practice. If a character is more or less a "stock character" with little in the way of distinctive features, then under US law, the character is not protected by copyright. If the character is distinctive, then the character is protected, and a new work using that character is a "derivative work" and requires permission just as much as a translation would, or a play (drama) version of a story, say. How distinctive is distinctive? that depends, and the only way to get a final decision is to be sued over it and have a court decide. Also, a parody of even a distinctive character is generally a 'fair use' and so is legal without permission, but what counts as a parody is also up to a court. Rules in other countries will be at least somewhat different.
As for the ethics of the matter, that is something about which opinions might differ. My view would be that if the original story is non-commercial, and especially if it is only a single story, not a long running series with a very well-established character, then I don't object to unauthorized sequels, if the author doesn't object and hasn't voiced such objections in advance. But creating a new, but similar character, is generally free of all such issues, and may be the better route to take. Some authors have explicitly consented to use of their characters, or of their settings, as Lurking Dragon did.